GENERALIZED HARMONIC NUMBER IDENTITIES AND A RELATED MATRIX REPRESENTATION
نویسندگان
چکیده
منابع مشابه
Generalized Harmonic Number Identities and a Related Matrix Representation
In this paper, we obtain important combinatorial identities of generalized harmonic numbers using symmetric polynomials. We also obtain the matrix representation for the generalized harmonic numbers whose inverse matrix can be computed recursively.
متن کاملTrust Modeling with Context Representation and Generalized Identities Trust Modeling with Context Representation and Generalized Identities
The majority of existing trust models is based on three underlying assumptions: (i) proven identity of agents, (ii) repetitive interactions and (iii) similar trusting situations. In our work, we address these assumptions by introduction of simple classification techniques in our mechanism that extends existing trust models, rather than by introduction of a new model. The proposed approach forma...
متن کاملRiordan arrays and harmonic number identities
Let the numbers P (r, n, k) be defined by P (r, n, k) := Pr ( H n −H (1) k , · · · , H (r) n −H (r) k ) , where Pr(x1, · · · , xr) = (−1)Yr(−0!x1,−1!x2, · · · ,−(r− 1)!xr) and Yr are the exponential complete Bell polynomials. By observing that the numbers P (r, n, k) generate two Riordan arrays, we establish several general summation formulas, from which series of harmonic number identities are...
متن کاملNew Harmonic Number Identities with Applications
We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums ∑n k=1 ∏r j=1Hk({1} ) when ∑r j=1 λj ≤ 5. We apply these identities to the study of two congruences modulo a power of a prime.
متن کاملHarmonic Number Identities Via Euler’s Transform
We evaluate several binomial transforms by using Euler's transform for power series. In this way we obtain various binomial identities involving power sums with harmonic numbers.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2007
ISSN: 0304-9914
DOI: 10.4134/jkms.2007.44.2.487